The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^2 - 2y^2 - 2 = 0$ to its asymptotes is:

If $|a|=1, |b|=2$ and the angle between $a$ and $b$ is $120^{\circ}$,then ${(a+3b) \times (3a-b)}^2$ is equal to

Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength $\lambda_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{\lambda_1}{2}$. The power radiated at $T_2$ is (in $P$)

Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. $A$ moves with uniform acceleration $a$ and $B$ moves with uniform velocity $V$. They meet after time $t$. The value of $t$ is:

The major product of the following reaction is

Consider the following gaseous equilibrium in a closed container of volume $V$ at $T \text{ K}$:
$P_{2(g)} + Q_{2(g)} \rightleftharpoons 2PQ_{(g)}$.
$2 \text{ moles}$ each of $P_{2(g)}$, $Q_{2(g)}$, and $PQ_{(g)}$ are present at equilibrium. Now, $1 \text{ mole}$ each of $P_{2}$ and $Q_{2}$ are added to the equilibrium while keeping the temperature at $T \text{ K}$. The number of moles of $P_{2}$, $Q_{2}$, and $PQ$ at the new equilibrium, respectively, are: